A priori bounds for superlinear problems involving the N-Laplacian

In this paper we establish a priori bounds for positive solutions of the equation−ΔNu=f(u),u∈H01(Ω), where Ω   is a bounded smooth domain in RNRN, and the nonlinearity f has at most exponential growth. The techniques used in the proofs are a generalization of the methods of Brezis and Merle to the N-Laplacian, in combination with the Trudinger–Moser inequality, the Moving Planes method and a Comparison Principle for the N-Laplacian.